Years ago I ditched my DLR's (Canon 6D and 7D) due to the weight and bulk. On tours you don't have time to change lenses as one moment you are doing a closeup and a second later you're doing a long shot. Over half of my shots are now taken on my iPhone 7+, and less are taken on my other travel Cameras (RX10-III and RX100-IV). I never even used the RX100 this last trip so I may not bother with it on my upcoming Peru trip. However it is great for capturing stage performances, such as a sunset dance in Bali when the iPhone zoom isn't sufficient. You can't hand hold a heavy DLSR with a long zoom for a 45 minute performance while sitting at a table, when tripods aren't allowed. Many times I compare the iPhone photos with the RX10 photos and due to superior light handling (especially HDR), the iPhone photo is better more than 50% of the time. I only display them on my 30" Cinema display and have no issue with image quality, given it's zoom limitations.
The iPhone is also great for things like taking shots on the tarmac as you are heading to a plane for boarding, food shots in restaurants or on the plane, all of those times when you only have a second to point and shoot.
I just ran the jf Data Explorer plugin in Lightroom on the pictures that I just took on a trip to some former parts of Italy in the Adriatic to see the distribution of my images. Supposedly the results were converted to full frame equivalents, but I don't think that's the case as it lists 11 shots at 600 mm and the RX10-III with a crop factor of 2.73 is actually shooting at 1638 mm so take the actual values with the grain of salt
Since a DX lens has a crop factor of 1.5 your lenses are full frame equivalents of:
Focal Length/Aperture Shots
52.5 2.7 5265 (24-52)
75 2.7 2096 (54-75)
27-157.5 5.25-8.4 790 (77-154)
105-315 419 (159-310)
1193 of the shots, or a bit less than 10% of the total, were shot with the widest lens available, as when capturing vistas from hilltop cities.
You mentioned that one of your lenses is 30 years old. Is it a film lens? Generally you don't get the best results using a lens designed for film on a digital camera.
So in summary if I had just 1 lens I'd go with the 27-157.5. For low light in museums I'd use my iPhone and skip the 52.5 2.7 since the zoom limitation doesn't exist there.
Potential IQ issues aside (iPhones can produce images with acceptable IQ depending on your needs), there are creative reasons where an iPhone or a camera with a larger sensor are better tools, specifically relating to depth of field (DOF) (i.e. how much of the image is in acceptable focus from front to back).
DOF is a function of several factors: focal length, aperture, camera-to-subject distance. Somewhat related is subject-to-background distance.
DOF is greater (i.e. more of the image is in acceptable focus) for shorter focal lengths, smaller apertures, greater camera-to-subject distance. DOF is smaller (i.e. the subject is sharp but the background is blurred) for longer focal lengths, larger apertures, smaller camera-to-subject distance, greater subject-to-background distance.
iPhones are great at creating good front-to-back sharpness at a larger aperture compared to a DX or FF sensor because the focal length of the lens is so small. This can have practical benefits for some subjects: in lowish light more of the image may be in acceptable focus.
iPhones are not good at creating subject isolation (i.e. blurring out the background) unless you get really close to the subject and the background is relatively far away.
For shooting interiors on a trip (like in a church/cathedral) or scenics at dawn/dusk the iPhone might be an acceptable tool as you want the large DOF with a large aperture to let in more light.
For museums it can be a poor tool as there are likely to be many distracting background elements that will detract from the composition, which you would like to be able to minimize by blurring them out to isolate the subject. Significantly harder to do this with an iPhone compared to a camera with a larger sensor (and thus a longer focal length lens achieving the same field of view).
Some subjects benefit from a large DOF. Some subjects need a shallow DOF.
I'm not saying an iPhone isn't an adequate camera for some situations or arguing that you need to carry around a DX or FF camera instead. But it's important to remember that all cameras/lenses are tools with their strengths and weaknesses. The key is finding the right tool for the job at hand